Question

Sue buys 5 notebooks and 3 binders for 21.56. Tim buys 4 notebooks and 2 binders for 15.80. how much is each item? How do I solve this??

Answer 1

let x= # of notebooks
let y= # of binders

\[5x+3y=21.56\]

\[4x+2y=15.8\]

Now do you know how to solve it?

Answer 2

I get that same set up but the next step is what I don't understand. I am told to multiply the top row by 4...4(5x+3y)=21.56 and the next row by -5(4x+2y)=15.80....why am I supposed to multiply by the 4 and -5?

Answer 3

Ah yes, you see, there are different ways to solve that, you are doing the elimination method. You multiply the top row by 4 to make 20x, and what ever the rest of the equation is multiplied by 4. You multiply the bottom row by -5 to get -20x, and whatever the rest of the equation is multiplied by -5. Then you add the 2 equations, so:

\[4(5x+3y)=21.56\]
\[=20x+12y=21.56\]


\[-5(4x+2y)=15.80\]
\[=-20x-10y=15.80\]

Then you add them:
20x+-20x=0
12y+10y=2y
21.56+15.80= 37.36

So:
\[2y=37.36\]
\[y=18.68\]

Then you plug that in to one of the original equations to find x

Answer 4

Sorry, I meant -12y+10y=2y

Answer 5

I was doing the elimination method and didn't know it. Thanks for the help, I really appreciate the help